Fredlund and Krahn Example Problem

The following example problem for verification is taken from the paper by Fredlund and Krahn, titled Comparison of slope stability methods of analysis, and is a simple 2H:1V slope, 40ft (12m) high. The slip center about which moments are calculated remains constant at (120,90).

The geometry for cases 1 and 2 are shown below. A description of all cases follows.

Case 1 Geometry

Case 2 Geometry

Case 1 - Simple 2:1 slope, 40ft (12m) high, Φ' = 20o, c' = 600 psf
Case 2 - Same as 1 with a thin, weak layer with Φ' = 10o, c' = 0
Case 3 - Same as 1 except with ru = 0.25
Case 4 - Same as 2 exception with ru for both materials
Case 5 - Same as 1 except with a piezometric line
Case 6 - Same as 2 except with a piezometric line for both materials

Published Results

Case

Ordinary

Bishop's Simplified

Janbu's Simplified (Corrected)

Spencer

Morgenstern-Price f(x) = constant

FOS

FOS

FOS

FOS λ

FOS λ

1

1.928

2.080

2.041

2.073 0.237

2.076 0.254

2

1.288

1.377

1.448

1.373 0.185

1.378 0.159

3

1.607

1.766

1.735

1.761 0.255

1.765 0.244

4

1.029

1.124

1.191

1.118 0.139

1.124 0.116

5

1.693

1.834

1.827

1.830 0.247

1.833 0.234

6

1.171

1.248

1.333

1.245 0.121

1.250 0.097

MacSlope Results

Case

Ordinary

Bishop's Simplified

Janbu's Simplified (Corrected)

Spencer

GLE f(x) = constant

FOS

FOS

FOS

FOS λ

FOS λ

1

1.929

2.078

2.022

2.076 0.261

2.076 0.259

2

1.299

1.381

1.431

1.378 0.168

1.382 0.176

3

1.608

1.761

1.711

1.760 0.252

1.754 0.250

4

1.039

1.122

1.166

1.121 0.152

1.125 0.154

5

1.695

1.831

1.807

1.827 0.236

1.826 0.240

6

1.173

1.242

1.306

1.240 0.115

1.245 0.124

The MacSlope calculated results are within 2.5% in all cases for all available methods.

Download the MacSlope file for case 6 of this verification example here.

Watch a tutorial video describing how to set up and analze the Fredlund and Krahn example problem below.